Orbital Mechanics 202

Continuing with the last post about orbits, in this post we will see the most relevant orbits. The first of them is Low Earth Orbits. Low Earth Orbits are those which have between 100 and 2000 kilometres of altitude, this is the region of space with the most satellites, as it is the closest operational region of space to Earth. The lowest altitudes are in the atmosphere of Earth and due to the air on it they are more unstable, and the motion of the satellites is braked by the atmosphere. The satellites in these orbits have a velocity of around 7 km/s and their orbit period, the time it takes to complete one orbit around Earth, is between 90 minutes and 2 hours. The International Space Station (ISS) has an average altitude of 400 kilometres and a period of 92 minutes, resulting in 16 sunrises and sunsets per day.

Figure 1. Low Earth Orbit.

The Geosynchronous Orbits (GSO) have an orbital period that matches Earth’s rotation on its axis, 23 hours, 56 minutes, and 4 seconds, which is one sidereal day. The synchronization of rotation and orbital period means that, for an observer on Earth’s surface, an object in geosynchronous orbit returns to the same position in the sky after a period of one sidereal day. These orbits have an altitude of 35,800 km and a velocity of 3 km/s. It is also used the Geostationary Orbit (GEO), referred to as a geosynchronous equatorial orbit, it is a circular geosynchronous orbit with an altitude of 35,800 kilometres and an orbital period of a sidereal day. Every satellite in a GEO orbit is geosynchronous, but a satellite in a GSO orbit is not necessarily geostationary. A satellite whose inclination is different from 0º, GEO, will appear to go up and down vertically or North South, while a satellite whose orbit is not perfectly circular, GSO, will appear to oscillate on the horizontal axis.

Figure 2. Geosynchronous Earth Orbit.

If we had an imaginary chalk line reel that tied the centre of the Earth and the satellites, the pattern that these two orbits, GSO and GEO, would leave on the surface of the Earth would be the ones found in the following image. The red line is the one generated by the GSO satellite and yellow line is the GEO satellite.

Figure 3. GEO and GSO patterns over Earth surface.

The orbits in the space between altitudes of Low Earth Orbit and Geosynchronous Orbit (GEO) are called Medium Earth Orbit (MEO), usually with an orbit period of around 12 hours and an altitude of 20,000 kilometres. These orbits main use is for geographic positioning systems (GPS, GLONASS, Galileo).

Figure 4. Medium Earth Orbit.

Apart from the LEO, MEO and GEO orbits we will also check other two more orbits that have interesting characteristics. Such as the Molniya orbit which is designed to provide communications and remote sensing coverage over high latitudes. It is a highly elliptical orbit with an inclination of 63.4 degrees, an argument of perigee of 270 degrees, and an orbital period of approximately half a sidereal day.

Figure 5. Molniya orbit.

Additionally, we have the Sun-synchronous orbit (SSO) which is a nearly polar orbit, in which the satellite passes over any given point of the planet’s surface at the same local mean solar time. It is an orbit arranged so that it precesses through one complete revolution each year, so it always maintains the same relationship with the Sun. These orbits usually have about 600–800 km in altitude, with periods of 100 minutes, and inclinations of around 98°.

Figure 6. Sun-synchronous orbit.

Apart from learning the orbit elements we will learn about how to put those satellites in orbit, how do we transport them from Earth’s surface to orbiting around it. In order to be able to overcome the force of gravity our spacecraft needs to increase its speed, this change of velocity is called Delta-v, symbolized as ∆v. It is a measure of the impulse per unit of spacecraft mass that is needed to perform a manoeuvre. It is a scalar that has the units of speed. ∆v is the change in velocity that can be achieved by burning a rocket’s fuel load, it is produced by reaction engines, such as rocket engines, and is proportional to the thrust per unit mass and the burn time.

The usual velocity of a LEO satellite is 7 km/s, consequently the ∆v applied to the spacecraft should be greater than that, and it is so because it will not only overcome the force of gravity but the aerodynamic drag of the atmosphere too, as the launcher has to get through all the thickness of the atmosphere.

Figure 7. Launch trajectory of a rocket launcher.

When choosing the launch site, it is important be as close to the Equator as possible, this way the launcher can use the gravity assist of Earth in order to help its flight. This procedure requires less fuel and resources, which equals in less cost and can also mean a bigger payload to insert in orbit.

Figure 8. Choosing the latitude of launch is very important.

In the following animation you can see the different steps of a rocket launch. It all begins with the vertical ascent, where the biggest amount of fuel is burnt as the launcher needs the to change its status from static to in movement, it is also the step where the rocket gets through the thickest layers of the atmosphere, where the aerodynamic forces against it are stronger.

The following step is the pitch over, where the rocket turns its engine slightly to direct some of its thrust to one side. This force creates a net torque on the ship, turning it so that it no longer points vertically. Then is the gravity turn, when the rocket uses gravity to steer the vehicle onto its desired trajectory, this is when the gravity assist happens and being closer to the Equator is so important.

The final step is the propulsion in the vacuum of space and there are no longer aerodynamic drag forces, consequently the fairing of the rocket is no longer useful, and the rocket can get rid of it. The spacecraft will end alone its arrival to the destination orbit with its own fuel, not being linked to the rocket anymore.

Figure 9. Stages of a launch.

And once the satellite has completed its mission for over 5,10, 15 years and its lifetime has come to an end, the same way that we recycle on Earth and we dispose our waste, we must put the satellite out of it orbit so the following satellites have space and do not stay forever orbiting around Earth control-less.

Figure 10. Evolution of space debris around Earth.

If the satellite is in LEO the best way to get rid of it is to propel it against the atmosphere, and it will burn through the atmosphere, being very improbable that any piece of it will land on Earth surface.

Figure 11. Satellite in LEO re-entering on Earth atmosphere.

If the satellite is in GEO, the best way to dispose it is to send it to a graveyard orbit. One significant graveyard orbit is a super synchronous orbit 200-300 km above geosynchronous orbit where many inoperative geosynchronous satellites rest.

Figure 12. Satellite in GEO getting into a graveyard orbit.

The next step in learning orbital mechanics is the motion of more complex space bodies systems, like the ones in the Solar System. We have studied all these orbits as if they were flat in 2D, but the Sun is moving along the Milky Way Galaxy and Earth is revolving too around the Sun. A very interesting animation is the last one of this article, which represents the Helical model of the Solar Systems and helps comprehend the mechanics of all the planets as a vortex, not a plane.

Figure 13. Helical model of the Solar System.

Jesús Lucero Ezquerro

Jesús Lucero Ezquerro

Analyst in Earth Observation